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kotegsom [21]
3 years ago
12

Find the inverse of the linear function y= 1/2x+3

Mathematics
1 answer:
Korvikt [17]3 years ago
3 0

Answer:  The inverse of the given function is y=2x-6.

Step-by-step explanation:  We are given to find the inverse of the following linear function :

y=\dfrac{1}{2}x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)

The inverse of y = f(x) is written as

x=f^{-1}(y).

Substituting the above in equation (i), we get

y=\dfrac{1}{2}x+3\\\\\Rightarrow y=\dfrac{1}{2}f^{-1}(y)+3\\\\\Rightarrow \dfrac{1}{2}f^{-1}(y)=y-3\\\\\Rightarrow f^{-1}(y)=2(y-3)\\\\\Rightarrow f^{-1}(y)=2y-6.

Thus, the inverse of the given function is y=2x-6.

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